You can’t remember your way to understanding hard stuff

Probably the most important short statement ever made about teaching and learning is this from Vygotsky.

As we know from investigations of concept formation, a concept is more than the sum of certain associative bonds formed by memory, more than a mere mental habit; it is a genuine and complex act of thought that cannot be taught by drilling, but can only be accomplished when the child’s mental development has itself reached the requisite level.

Which brings me back to the recommendations of EEF and its misunderstandings about ‘metacognition’, which do indeed focus on associative bonds formed by memory and mental habits. And that’s the problem.

Here are simplified versions of Newton’s Laws of Motion.

First Law

A body remains motionless or continues to move in a straight line at constant speed unless subject to an external force

Second Law

Force = Mass x Acceleration

Third Law

Every action has an equal and opposite reaction

Now match the following counter-intuitive phenomena to the appropriate Law.

A – Small, heavy-ish objects of different weights simultaneously dropped from the same height, hit the floor together

B – A child riding in a child’s seat on the back of mum’s bike cannot help her pedal up-hill by pushing on her bum

C – Above a few hundred metres, if you jump out of an aeroplane at a great height you hit the ground at the same speed as you would if you jumped from half the height.

If you are struggling, ask yourself how helpful it is to remember the three Laws of Motion by heart. Not helpful at all right? (answers: A – 2nd Law, B – 3rd Law, C – 1st Law).

Why did it take hominids more than a million years to notice that large, heavy rocks and small, light ones fall to earth at the same rate when dropped?

It is because it’s so profoundly counter-intuitive, which is the same reason why modern school students can’t understand it either, despite the well recorded efforts of Galileo (between 1589 and 1592), and successive generations of their  teachers making them memorise Newton’s Laws of Motion. (His Principia was published in 1687).

This is the reason.

Hold a heavy weight in your hand above a table. It presses down on your hand with a large force right? Now get your friend to push down on your empty hand with a similar large force. Then suddenly take your hand away. Your friend’s hand then crashes down onto the table. The harder your friend was pushing down, the faster his hand crashes down when you take your hand away. So it’s the same when holding heavy objects – the heavier they are, the greater the force on your hand and so the faster they ‘crash down’ when you release them.

Except that it isn’t: but why not?

It’s all to do with Piaget and the transition between Concrete and Formal Operational Thinking. Concrete stage minds can cope with one independent variable at a time. Hanging a heavy weight on a spring stretches it more than does a lighter weight (Hooke’s Law). Larger masses (kilograms) have a larger downward force of gravity (newtons) on them. This is called the weight of the object. How much things weigh depends on the strength of gravity g, which is the gravitational force (newtons) per kilogram of mass. On earth, gravity makes one kilogram weigh 9.8 newtons. If you  hold more kilograms in your hand the weight increases, just as a spring stretches more if you hang a bigger weight on it. Students that have reached Piaget’s Concrete stage are capable of understanding one on one patterns like this if taught competently.

Dropping objects is more complicated than this because there are two variables operating simultaneously. Two variables take the level of difficulty into the Formal Operational stage. Unless the minds of such students have reached this developmental level, they will not be able to construct personal mental models that make sense because their personal schema are not up to the job. This is the proper ‘constructivist’ meaning of ‘metacognition’ – consciously thinking about how to make sense of unexpected observations.

Alex Quigley, in the sixth instalment of his EEF ‘metacognition’ series, discusses ‘long term memory’, ‘cognitive load theory’ and chunking’. The idea is that to aid long term memorising you must not give the learner too much to learn in one go. Instead you should chop it into ‘chunks’. This really isn’t a profound idea worthy of a ‘learning theory’.

I am sure it is good advice if you want a student to memorise stuff, but it won’t of itself bring about understanding. To quote Vygotsky, such high level understanding can only be accomplished when the child’s mental development has reached the requisite level. The real value of ‘metacognition’, lies in its power to help students develop their cognition from the concrete to the formal level (so they can understand it), not in helping them remember stuff. This is because without a conceptual framework that is up to the job, no amount of memorising brings about understanding.

So what are the two variables involved in dropping things?

The first is the weight of the object.

The second is its inertia. What’s that? Where did that come from? It too, comes from Newton’s 2nd Law of motion.

Force (weight) = Mass x Acceleration.

This tells you how much force is needed to get an object moving.

Change it round to Acceleration = Force/Mass and you see that larger masses (which weigh more) also take more force to get them moving. This resistance to moving is called the inertia of the object.

So you there you have your two variables, weight and inertia, and what’s more they cancel each other out, so heavy objects have lots of gravitational force on them, but they also have lots of inertia, so the extra inertia cancels out the heavier weight so all objects (that do not have significant air resistance) fall at the same rate.

What is that ‘same rate of fall’ for all objects? It is ‘g’, the strength of gravity (newtons per kilogram), whose equivalent units are metres per second squared, which is the unit of acceleration.

How beautifully brilliant is that? Why wouldn’t any student get an orgasmic flush of pleasure from realising that? It is what Archimedes must have felt when he leapt from his bath having suddenly understood the principle of flotation. What a fantastic job it is to lead school students to such insights; and not just science and maths students. For example, see the work of Deborah Kidd in the humanities and other subjects.

But such understanding does not accrue at a steady rate as more and more knowledge is emptied by the teacher into the mind of the student, like filling a bucket. It is important to note the experience of the student when taught on the knowledge/memory-based model. The teacher expects the student to gradually accrue more and more understanding with each ‘chunk’ of new knowledge shovelled in. EEF measures this process in ‘months of progress’.

But, unless the cognitive framework of the learner can assimilate the new knowledge in a way that makes sense to the learner, it is unlikely that there will be any growth of understanding. I don’t want to go all Marxist, but learning is a ‘dialectical’ process that arises from the tensions that contradictions cause in the mind (cognitive dissonance). Metacognition is the conscious process of thinking about such personal contradictions, so becoming able to express them to peers, and to debate the metacognition that others are able to express. This is a powerful learning process. It does not result in incremental gains over months, but sudden, joyous leaps of personal insight – altogether a more rewarding experience that builds motivation at the same time as expanding the general cognitive capability of the learner. This is the principle of ‘plastic intelligence’.

The importance of hands-on practical work

On 21 November 2013, OfSTED published a report entitled, Maintaining curiosity: a survey into science education in schools. They found that dull teaching – accompanied by a lack of practical work in the subject – was putting pupils off the science subjects. In some schools, not enough time had been set aside in the timetable for pupils to do practical work. Girls, in particular, were likely to ditch physics – with only 11,390 going on to do it in the sixth-form in 2011 despite 159,745 getting two good GCSE passes in science. In addition, a minority of secondary schools were ‘pre-occupied with tests and examination results as ends in themselves’ rather than aiming to improve pupils’ deeper knowledge of the subject. The report points out that getting good grades in science is not necessarily the same as “getting” science.

Since 2013 there has certainly been no improvement. I wrote about this in March 2017 and since then things have only got worse, with the shortage science teachers now dire, compounded by concerns about quality and experience, with so many teachers now ‘trained’ on the job in Academy MATs where practical science is getting ever rarer. I also wrote about the importance of practical work here.

I was fortunate to start my teaching career in 1971, just as schools were being lavishly equipped with the brilliantly designed apparatus for the new Nuffield Science courses. This equipment remained the mainstay of science practical work right up to my retirement in 2003, after 32 years of continuously teaching GCE, CSE, GCSE and A Level for the whole of that period.

In 1981/82, Along with many other Leicestershire LEA teachers, I was seconded onto the Leicester University M.Ed Studies course (full time, on full pay, with expenses). It was here that I became aware of the work of Philip Adey and Michael Shayer, who both had prior associations with Leicester University. We were taught about their work in developing the Cognitive Acceleration through Science Programme (CASE). Adey and Shayer were science teachers that had become obsessed with the problem of difficulty. Why is it that some students can understand hard stuff and some can’t? They realised that the answer is primarily to do with the current cognitive ability of the student, not their motivation, work rate, dedication or exposure to ‘memory aids’ and disciplines of the sort advocated by EEF. CASE is about teaching for cognitive development and understanding, rather than passing memory tests. It is still going strong.

After ten years of teaching science, this made immediate sense to me, so I bought their book, ‘Towards a Science Teaching’ (1981)This includes an annex containing their Curriculum Analysis Taxonomy that classifies the cognitive demand of scientific topics/concepts on a Piagetian scale 1-Pre-operational, 2A-Early Concrete, 2B-Late Concrete, 3A-Early Formal, 3B Late Formal.

For my M Ed dissertation I decided to test if this taxonomy was robust in practice. I recruited four experienced Heads of Science (plus myself) to use the taxonomy to rate the cognitive demands of the syllabus items in each of three ‘General Science’ CSE exam courses. My most important objective was to produce a statistical calculation of the degree of agreement between the five raters. I managed to gain the interest of Michael Shayer in this work and he helped me with the statistics of reliability. The result was that the raters agreed to a high degree, thus providing strong support for the validity and pedagogic utility of both Piagetian theory and its application to classroom practice.

There was much else in the results that was discussed in my dissertation, including the degree of ‘cognitive matching’ of the syllabus items to the likely distribution of Piagetian Levels in secondary school populations that had been determined by earlier work of Shayer and Adey. They had previously done their own analysis of the cognitive demand of GCE, Biology, Chemistry,  and Physics syllabuses and found a large mismatch with the likely cognitive ability distributions in the schools.

Nearly 40 years later this remains a crucial, issue for schools and their teachers. The difference now is that nobody at the DfE, OfSTED, EEF or anybody else supported and funded by the DfE has any interest in it, because the knowledge-based approach required by the ideology  of marketisation misunderstands the true relationship between teaching, learning and understanding.



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2 Responses to You can’t remember your way to understanding hard stuff

  1. Jennifer Hawkins says:

    Thank you Roger – this is a fascinating and informative article. I would recommend not only teachers, but also psychologists to consider what you say because it demonstrates how we need to gather collaborative research data about the subjects/learners feelings and look at their behaviour – asking about and noting their own perceptions/analyses of their learning. I am exploring texts on memory and have been looking at cognitive load theory, which to me on first exploring seems at base simplistic although clad in academic rhetoric. I am about to read and can confidently recommend: “Adventures in Memory: the Science and Secrets of Remembering and Forgetting” 2018 by Norwegian authors Hilde and Ylva Ostby – interesting combination – a neuro-scientist and a novelist – sisters.

    The points you make also made me challenge my unconscious assumptions about myself hopefully informing my current research into the roles of emotions and feelings in thinking. I will be reading it again! My own cognitive concepts/abilities in science and maths are very underdeveloped even with a father who was an industrial chemist/factory manager – no natural flair in those subjects to his dismay. I can also relate this to the strict knowledge delivery approach of my own schooling – any exams I did ‘get’ – few and far between – were down to short term visual memory/cramming and forgetting revising system for exams. This was considered as sufficient to prove intelligence in my school days (50’s, 60’s) even when everything was forgotten the next day! Questions were deemed unnecessary or a sign of rebellion – I was full of them – I found learning very frustrating, because my polite but tricky questions were mostly dismissed. My parents had they lived that long would have been astonished to hear I would eventually achieve a PhD by research. I would be interested to hear other educationalists’ story data on this subject.


  2. When arguments and evidence from different academic cultures produce mutually supportive conclusions, then those conclusions gain in credibility. I argue here and in many of my articles on this website that the imposition of a marketisation culture on the English education system has brought with it an unavoidable baggage of perverse incentives that damage the quality of the teaching and learning experience for both teachers and students, while steadily degrading deep learning and understanding. This has come to be called the ‘Anti-Flynn Effect, which you can read about it here.

    I write from the culture of science education, but this article by Valerie Coultas, from the sociology of education culture recently published on the ‘Reclaiming Schools’ website, despite the unfamiliar terminology, has me nodding in agreement. I strongly recommend it.


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